Question

Two mirrors are inclined at an angle $\theta$ as shown in the figure. Light ray is incident parallel to one of the mirrors. The ray will start retracting its path after third reflection if?

• A. $\theta ={45}^o$
• B. $\theta ={30}^o$
• C. $\theta ={60}^o$
• D. All three

Answer 1

The correct option is B $\theta ={30}^o$

Let $MN$ and $AB$ parallel to $MN$ is incident on $MP$ and the ray after third reflection on $MP$ at B retraces its path as shown in the diagram. Hence $CD$ is perpendicular to $MP$.

This means $\angle BCN=\angle DCM={90}^{\circ }-\theta$

$AB||MN$ and $BC$ is the intercept.

So$\angle PBA=$ corresponding $\angle PBN=\theta$

And $\angle ABC={180}^{\circ }-2\theta$

Since $AB\parallel MN$ and BC is the intercept

$\angle ABC+\angle BCN=180\circ$

$\Rightarrow 180\circ -2\theta +90\circ -\theta =180\circ$

$\Rightarrow 3\theta =90\circ$

$\Rightarrow \theta =\frac{{90}^{\circ }}{3}3=30\circ$

Answer C: